\(\dfrac{2^{2024}+2^{2023}+2^{2022}+2^{2021}}{60}=\dfrac{2^{2021}\left(2^3+2^2+2+1\right)}{60}=\dfrac{2^{2021}.15}{60}\)

\(=\dfrac{2^{2019}.2^2.15}{60}=\dfrac{2^{2019}.60}{60}=2^{2019}\)

\(\Rightarrow n=2019\)

-6/x=0.5

x=-6/0.5

x=-12

5b.

\(\dfrac{a}{b}>\dfrac{4}{7}\Rightarrow7a>4b\) \(\Rightarrow14a>7a+4b\)

\(\Rightarrow14a>1994\Rightarrow a>\dfrac{997}{7}>142\)

\(\dfrac{a}{b}< \dfrac{2}{3}\Rightarrow2b>3a\Rightarrow4b>6a\) \(\Rightarrow7a+4b>13a\)

\(\Rightarrow13a< 1994\Rightarrow a< \dfrac{1994}{13}< 153\)

\(\Rightarrow142< a< 153\)

Lại có: \(7a+4b=1994\Rightarrow7a-14=1980-4b\)

\(\Rightarrow7\left(a-2\right)=4\left(495-b\right)\)

Do 7 và 4 nguyên tố cùng nhau \(\Rightarrow a-2\) chia hết cho 4 \(\Rightarrow a-2=4k\)

\(\Rightarrow a=4k+2\)

Mà \(142< a< 153\Rightarrow\left[{}\begin{matrix}a=146\\a=150\end{matrix}\right.\)

- Với \(a=146\Rightarrow7.146+4b=1994\Rightarrow b=243\)

\(\Rightarrow\dfrac{a}{b}=\dfrac{146}{243}\)

- Với \(a=150\Rightarrow7.150+4b=1994\Rightarrow b=236\)

\(\Rightarrow\dfrac{a}{b}=\dfrac{150}{236}\)

Vậy phân số cần tìm là \(\dfrac{146}{243}\) hoặc \(\dfrac{150}{236}\)

a) 2.4 = 1.8

⇒ 2/1 = 8/4

2/8 = 1/4

1/2 = 4/8

9/2 = 4/1

b) (-2).6 = 3.(-4)

⇒ -2/3 = -4/6

-2/(-4) = 3/6

3/(-2) = 6/(-4)

-4/(-2) = 6/3

c) -18.(-5) = 9.10

⇒ -18/9 = 10/(-5)

-18/10 = 9/(-5)

9/(-18) = -5/10

10/(-18) = -5/9

Từ các số 2; 3; -6; -4; -9 ta có:

2.(-9) = 3.(-6) và 2.(-6) = 3.(-4)

*) 2.(-9) = 3.(-6)

⇒ 2/3 = -6/(-9)

2/(-6) = 3/(-9)

3/2 = -9/(-6)

-6/2 = -9/3

*) 2.(-6) = 3.(-4)

⇒ 2/3 = -4/(-6)

2/(-4) = 3/(-6)

3/2 = -6/(-4)

-4/2 = -6/3

\(D=\dfrac{8}{3.11}+\dfrac{8}{11.19}+...+\dfrac{8}{187.195}\)

\(=\dfrac{11-3}{3.11}+\dfrac{19-11}{11.19}+...+\dfrac{195-187}{187.195}\)

\(=\dfrac{1}{3}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{19}+...+\dfrac{1}{187}-\dfrac{1}{195}\)

\(=\dfrac{1}{3}-\dfrac{1}{195}\)

\(=\dfrac{64}{195}\)

\(M=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{99.101}\)

\(=\dfrac{3-1}{1.3}+\dfrac{5-3}{3.5}+\dfrac{7-5}{5.7}+...+\dfrac{101-99}{99.101}\)

\(=\dfrac{3}{1.3}-\dfrac{1}{1.3}+\dfrac{5}{3.5}-\dfrac{3}{3.5}+\dfrac{7}{5.7}-\dfrac{5}{5.7}+...+\dfrac{101}{99.101}-\dfrac{99}{99.101}\)

\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{99}-\dfrac{1}{101}\)

\(=1-\dfrac{1}{101}\)

\(=\dfrac{100}{101}\)

Tui đang cần gấp mong người giúp !

\(a,\dfrac{5}{3}.x-\dfrac{2}{5}=\dfrac{1}{4}\\ \Rightarrow\dfrac{5}{3}.x=\dfrac{13}{20}\\\Rightarrow x=\dfrac{39}{100}\\ b,\dfrac{4}{7}.x-\dfrac{8}{5}=\dfrac{1}{2}\\ \Rightarrow\dfrac{4}{7}.x=\dfrac{21}{10}\\ \Rightarrow x=\dfrac{147}{40}. \)

a. \(\dfrac{5}{3}\).x . \(\dfrac{-2}{5}\) =\(\dfrac{1}{4}\)

    \(\dfrac{5}{3}\).x          = \(\dfrac{1}{4}\) : \(\dfrac{-2}{5}\)

    \(\dfrac{5}{3}\).x          = \(\dfrac{1}{4}\) . \(\dfrac{5}{-2}\)

    \(\dfrac{5}{3}\).x          =\(\dfrac{5}{-8}\)

        x          = \(\dfrac{5}{-8}\) : \(\dfrac{5}{3}\)

        x          = \(\dfrac{5}{-8}\) .\(\dfrac{3}{5}\)

       x           = \(\dfrac{3}{-8}\)

b.\(\dfrac{4}{7}\).x - \(\dfrac{8}{5}\)    = \(\dfrac{1}{2}\)

   \(\dfrac{4}{7}\).x          = \(\dfrac{1}{2}\)+\(\dfrac{8}{5}\)

   \(\dfrac{4}{7}\).x          = \(\dfrac{21}{10}\)

       x          = \(\dfrac{21}{10}\) : \(\dfrac{4}{7}\)

       x          = \(\dfrac{147}{140}\)

TK nha !!!

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